Talk:Inverse image functor

some of the -1's have come out as 1's I don't know how to fix this 129.215.104.170 (talk) 17:35, 12 October 2009 (UTC)

Contravariant is Confusing in this Context

The first sentence of the article is confusing. I think it should be rewritten as "In mathematics, the inverse image functor is a contravariant construction on topological spaces that induces a covariant functor on sheaves".

To explain, I believe the author is trying to say that if we have continuous maps $f\colon X\to Y$ and $g\colon Y\to Z$ then $(g\circ f)^{-1}=f^{-1}\circ g^{-1}$. However, for a fixed ringed space morphism $f\colon X\to Y$, $f^{-1}:\operatorname {Ab} (Y)\to \operatorname {Ab} (X)$ is actually a covariant functor. This difference makes the first sentence confusing. Nrekuski (talk) 01:49, 6 December 2019 (UTC)

An inverse image functor is a *covariant* functor while the formation of an inverse image functor is contravariant. I agree the first sentence is confusing; I have added a clarification but the first sentence should be rewritten, though I’m not completely sure how. — Taku (talk) 23:12, 12 December 2019 (UTC)

Notation

Why is the inverse image functor on sheaves called $f^{-1}$ here (except in one instance) and called $f^{*}$ elsewhere, e.g. in the sidebar and the page on the six operations formalism? I think $f^{*}$ is more standard. Let's at least be consistent within Wikipedia! John Baez (talk) 21:40, 1 September 2024 (UTC)

Because in algebraic geometry, the sheaf-theoretic inverse image is denoted by $f^{-1}$ while the module-theoretic one by $f^{*}$. We can’t change this since it’s quite standard even if it might conflict with the notations elsewhere. —- Taku (talk) 07:53, 2 September 2024 (UTC)